Solve for $r$, $ \dfrac{7}{r} = -\dfrac{9}{3r} - \dfrac{4r - 7}{r} $
Explanation: First we need to find a common denominator for all the expressions. This means finding the least common multiple of $r$ $3r$ and $r$ The common denominator is $3r$ To get $3r$ in the denominator of the first term, multiply it by $\frac{3}{3}$ $ \dfrac{7}{r} \times \dfrac{3}{3} = \dfrac{21}{3r} $ The denominator of the second term is already $3r$ , so we don't need to change it. To get $3r$ in the denominator of the third term, multiply it by $\frac{3}{3}$ $ -\dfrac{4r - 7}{r} \times \dfrac{3}{3} = -\dfrac{12r - 21}{3r} $ This give us: $ \dfrac{21}{3r} = -\dfrac{9}{3r} - \dfrac{12r - 21}{3r} $ If we multiply both sides of the equation by $3r$ , we get: $ 21 = -9 - 12r + 21$ $ 21 = -12r + 12$ $ 9 = -12r $ $ r = -\dfrac{3}{4}$